Groups

Hey, I am not entirely sure if I am doing this right. But anyways...
The directions say...

"Determine whether the binary operation * defined on the given set results in a group."
(A group is classified by 3 properties:
Associative Law a * (b * c) = (a * b) * c
Existence of an Identity: There exists an element, e, such that
a * e = e * a = a
Existence of Inverses: For each element, a, there exists an element, s,
such that a * s = s * a = e (the identity)

Hey, I am not entirely sure if I am doing this right. But anyways...
The directions say...

"Determine whether the binary operation * defined on the given set results in a group."
(A group is classified by 3 properties:
Associative Law a * (b * c) = (a * b) * c
Existence of an Identity: There exists an element, e, such that
a * e = e * a = a
Existence of Inverses: For each element, a, there exists an element, s,
such that a * s = s * a = e (the identity)